The $n\text{th}$ partial sum of the series $\sum\limits_{n=1}^{\infty }{{{a}_{n}}}$ is given by ${{S}_{n}}=\frac{8n}{n+5}$. $\sum\limits_{n=1}^{11}{{{a}_{n}}}=$
Explanation: $\sum\limits_{n=1}^{11}{{{a}_{n}}}~~~$ is the same as $~~~{{S}_{11}}\,$. ${{S}_{11}}=\frac{8\cdot 11}{11+5}=\frac{8\cdot 11}{16}=\frac{11}{2}$